Hello FreeCAD Community,
I am trying to assemble my first group.
When trying to import the parts, no files are shown at all.

When I first tried to save the seperate files I already had the problem, that they were saved as a .zip and couldn't be opened at all.
I figured out that I have to add the ending .fcstd manually for it to be compatible.
But even then the file can be only opened per double click and not via the GUI because it just is not visible.

You have either fumbled manually in the FreeCAD info or you have a very outdated version. If it's the latter, please update to a current version. For the new assembly stuff it might even be neccessary to use 0.18 (not sure about this).

It is not just the 'new assembly' stuff that is not working.
It is the basic 'open' command.
I was just able to work around it by double clicking the .fcstd
but that is not an option for the assembling, since more than just one file is needed.
I didn't changed anything manually since I used the programm for the first time.
And the version is the most recent 0.17 from the application manager
so it should be compatible to my OS.
I don't think that the experimental version is needed to use a basic function like
open or import.

that's a weird combination... Python2 goes often with Qt4, and Qt5 with Python3. And yet OCC 7.3.0 is nearly the latest release, with the stable 0.17 ... where did you get your FreeCAD from ? Did you try the latest shiny version ? That's the one I — and many others here around — are using.

And the version is the most recent 0.17 from the application manager
so it should be compatible to my OS.
I don't think that the experimental version is needed to use a basic function like
open or import.

Your version is not a stable version either. The fact that some software manager offers it for installation doesn't make things better. Have a look at https://www.freecadweb.org/wiki/Install_on_Unix and install either current 0.17 or as said before 0.18. Noone here knows which bugs your version has, there have been almost 8000 improvements from yours to the current stable 0.17. If you don't want to use something experimental, don't use that version.

Did you try the latest shiny version ? That's the one I — and many others here around — are using.

Nothing wrong with realthunder's version, but it should strongly pointed out that this is a fork of the official version. It may not work the same as the latest official version. I do not think it is regularly rebased, so it does not have a lot of the recent fixes in the official master version.

(Yes, I have a copy of the latest shiny version, but I also have a very recent copy of the official version.)

You have either fumbled manually in the FreeCAD info or you have a very outdated version.

Deep in the FreeCAD source, there is a file (don't remember which, or where) that fills the version info with arbitrary values if the Version.h file is not built successfully. The default revision number used to be 5235, I believe it was changed recently.

I think this numbering happens with Linux distribution packages that strip the Git history from the FreeCAD source before compiling the package, or do not use Git as build dependency; as the mechanism to extract the FreeCAD info relies on Git tools.